A discrete-ordinate weak Galerkin method for radiative transfer equation

TL;DR

This paper introduces a novel numerical method combining discrete-ordinate and weak Galerkin techniques to solve the radiative transfer equation, providing stability and error analysis supported by numerical experiments.

Contribution

It develops a new discrete-ordinate weak Galerkin method for radiative transfer equations with proven stability and error estimates.

Findings

The method is stable under the proposed norm.

A priori error estimates are established.

Numerical experiments confirm theoretical results.

Abstract

This research article discusses a numerical solution of the radiative transfer equation based on the weak Galerkin finite element method. We discretize the angular variable by means of the discrete-ordinate method. Then the resulting semi-discrete hyperbolic system is approximated using the weak Galerkin method. The stability result for the proposed numerical method is devised. A priori error analysis is established under the suitable norm. In order to examine the theoretical results, numerical experiments are carried out.